The information bit error rate (BER) in classical error coding is based on the Hamming distance, i.e. the number of bits that are different between the symbols at the transmitter and the decoded symbols at the receiver. For this metric, the positions of the source bits where the error occurred are not significant. This is unsatisfactory since in many scenarios all source bits are not equal and have different significance. For instance, representing an integer in binary, the bits will have different significance with the difference increasing exponentially with its position, and an error in the most significant bit is much more problematic than an error in the least significant bit.
Furthermore, the relationship between the difference |i−j| of two integers i and j and the Hamming distance when expressed as bitstrings is nonlinear and nonmonotonic. For instance, the difference between the numbers 8 and 7 is 1, but expressed as bits, their Hamming distance is 4. On the other hand, the difference between 0 and 2k is 2k, but have a Hamming distance of 1. In image compression, the discrete cosine transform (DCT) coefficients for lower frequencies are more important than the higher frequencies coefficients and luminance coefficients are more important than chrominance coefficients as the human visual system exhibits low-pass behavior and is more sensitive to luminance changes. In stored program computers, the program code is more critical than data as an erroneous instruction can cause the machine to crash whereas incorrect data typically leads to incorrect results, but not cause a machine to crash.